Regression-Based Tests for Moderation
Brian K. Miller, Ph.D.
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Presentation Objectives 1. Differentiate between mediation & moderation 2. Differentiate between hierarchical and stepwise regression 3. Run and interpreting hierarchical regression in SPSS 4. Compute interaction terms 5. Mean center variables 6. Graphing interactions
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1 1. Differentiate between mediation and moderation
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Moderation vs. Mediation § ______: third variable that affects strength of relationship between two other variables § Ex: relationship between performance and salary ______gender
§ Ex: relationship between X1 and Y is strong, especially if X2 is also strong § ______: third variable that acts as ______between two other variables § Ex: performance mediates relationship between job knowledge and salary
§ Ex: X1 “causes” X2 which “causes” Y
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2 ______Diagram
______
Predictor Criterion
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______Diagram
Predictor ______Criterion
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3 2. Differentiate between hierarchical regression & stepwise regression
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Hierarchical Regression § Variables entered in equation at various stages § Important statistics and tests § Change in R2 (i.e. ______) § Change in F-score (i.e. ΔF) § Overall equation ______§ Uses: § ______variables § Interaction terms § NOT same as ______regression
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4 Stepwise Regression § All variables entered at one stage § Software enters every ______of variables § Seeks to ______R2 § Capitalizes on chance characteristics of THIS sample L § Like throwing spaghetti against the wall to see what sticks L § Not recommended ______by some journals
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3. Run hierarchical regression in SPSS
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5 SPSS Example #1 § Click “Analyze” / “Regression” / “Linear” § Choose “DV1” as Dependent Variable § Choose “Control1”, “Control2” as IVs § Is there theoretical rationale for these control variables? § However, no need for stated hypotheses § Click “Next” § Choose “IV1”, “IV2” as Independent Variables § Click “Statistics” § Put check in box for “R squared change” § Click “Continue”, click “OK”
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6 4. Compute Interaction Terms
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Review Diagram
______
IV 1 DV 1
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7 Reconceptualizing Diagram as 2 x 2
IV 2 High Low High High ______DV Medium DV IV 1 1 IV
Medium DV ______DV Low 15
Caution! § Never ______continuous variables (e.g. cutting in half at the median) § Results in loss of useful information § Treats scores close to each other as if far from each other § In ______, no need to dichotomize since all IVs are categorical § ______subsumes ANOVA § But, different method of creating interaction terms needed
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8 Problem: ______Continuous Variable # Observations # Observations
10 1 5 6 17 DV Scores
Moderation Effects § Strength of relationship between IV and DV ______Moderator § If one is low on the moderator (IV2) the correlation between IV1 and DV is different from same correlation for those high on moderator (IV2) § In regression § correlations manifest themselves as ______, or § ______of lines § So…slope of lines is different based upon gender § Caution: Moderating variables is ALSO an IV
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9 Moderation Effects (cont’d) § MUST include bot______(i.e. both IVs) in regression before including ______(cross product of IV1 and IV2) § Hierarchical regression model 1 has both main effects but NO interaction term § Hierarchical regression model 2 has main effects PLUS interaction term 19
Example Hypothesis 1. There is an interaction effect between IV1 and IV2 in the prediction of DV, such that high levels of IV1 combined with high levels of IV2 will lead to higher levels of DV than will low levels of either or both of IV1 and IV2.
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10 Alternatively Written Hypotheses 2. The strength of the relationship between IV1 and DV depends upon IV2, such that IV1 is strongest when IV2 is high and weakest when IV2 is low. 3. There is a positive relationship between IV1 and DV especially if IV2 is also high.
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Plotting Interactions
______(r = .6)
DV
______(r = -.2)
IV1 22
11 Creating Multiplicative Terms § Most (but not all!) IVs in regression are ______§ For 2 IVs, create third term that serves as interaction § Simply ______both IVs to create new term § Heads up: sometimes new term is ______with component terms
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Collinearity Issues § Product of two variables is almost always collinear with its ______§ When two variables are so strongly correlated with each other that they affect interpretation of regression § Can make ______exceed ± 1.0 L § Tolerance / ______(VIF) § Tolerance is reciprocal of VIF § Collinearity indicated if: § Tolerance < .10, or… § …VIF > 10
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12 SPSS Example #2: Moderated Multiple Regression § Click Analyze/Regression/Linear or Dialog Recall button § Click “Reset” to start with all new variables (i.e. remove the control variables previously used) § Choose “DV1” as DV § Choose “IV1” and “IV2” as IVs § Click “Next” § Choose new term “IV1xIV2” (interaction term already created from product of two IVs above) as only IV in second step of hierarchical regression model § Click “Statistics” § Put check in boxes for “R square change” and “Collinearity Diagnostics” § Click “Continue”, click “OK” 25
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13 5. Mean Centering Variables
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Mean Centering Variables § Mean centering of variables reduces impact of ______§ This is NOT same as ______variables! § Allows for better interpretation of regression weights § Requires: § Calculation of ______of the variable § Creation of new variable that… § …is ______between measured variable and mean of variable
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6. Graphing Interactions
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16 Graphing Interactions § DV on ______(Y) axis § IV on ______(X) axis § Calculate values of Moderator (other IV) 1 sd above and below mean § Calculate values of IV 1 sd above and below mean § Insert value of Moderator at lower sd in ______§ Insert value of Moderator at upper sd in regression equation
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Using Regression Formula to Plot Interactions Use the regression equation:
Y = 2.708 - .667IV1 - .333IV2 + .481IV1IV2
Find 4 different values (points) for Y
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17 Using Regression Formula (cont’d) § Calculate one equation for: § Insert value of IV2 at 1sd above mean § Insert value of IV1 at 1sd above mean § Calculate another equation for: § Insert value of IV2 at 1sd below mean § Insert value of IV1 at 1sd below mean § Calculate one equation for: § Insert value of IV2 at 1sd above mean § Insert value of IV1 at 1sd below mean § Calculate another equation for: § Insert value of IV2 at 1sd below mean § Insert value of IV1 at 1sd above mean
§ Connect the dots (i.e. draw the line segments) 35
Sample Graph
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4.5
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3 Low IV2 High IV2 Dependent variable Dependent variable 2.5
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1.5
1 Low IV1 High IV1
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18 Using Online Calculators Instead § See http://www.jeremydawson.co.uk/slopes.htm
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19 Things We Learned 1. Mediation and moderation are very different 2. Hierarchical regression is NOT stepwise regression 3. Interpreting hierarchical regression output is easy 4. Computing interaction terms is just simple multiplication 5. Mean centered variables offset collinearity 6. Graphing interactions is easier with Excel
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That’s all folks!!!
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